Question

find the value of k for which the pair of linear equation X + 3 Y is equal to K - 21, 12 x + Y is equal to K has no solution

Answer 1

x +3y = k - 21
12x + y = k

(two lines do not have solution when they are parallel to each other and given are the equations of two lines)

we know that for no solution
$\frac{a1}{a2} = \frac{b1}{b2} \: not = \frac{c1}{c2}$
therefore

1/12 = 3/1 not = (k-21)/k

therefore, I taking any one condition we get

3 not= (k-21)/k

3k not= k-21

2k not= -21

K not= -21/2

therefore, we get

the final answer as

the pair of linear equations have no solution for
K not equal to -21/2
else for all K the equations have solution

hope this answer will be helpful to you